This invention relates generally to the field of industrial process control, and particularly to a method for rapidly controlling a measured variable of a process from an existing value to a very divergent desired value without an overshoot beyond the new value.
Analog Controllers
An analog controller receives a continuous analog signal input that represents a measured process value or variable (PV) from a sensor and compares this value to the desired value setpoint (SP) to produce an error signal (ES). The controller uses this error to calculate any required correction and sends a continuous analog signal output (control variable), to a final control element (any continuously variable valve, damper, pump, fan, etc.). The final control element (FCE) then controls the process variable.
Proportional-Integral-Derivative (PID)
The original analog controller had only Proportional, or gain, control. This controller compared the process variable to the setpoint and varied the control variable as a Docket 172.02 selected multiplication value, which could be more or less than one. Because the amount of control variable change, due to deviation of the process variable from the setpoint, decreased as the process variable neared the setpoint, the process variable could continue to deviate (droop) from the setpoint indefinitely. To overcome this it was necessary to manually offset the setpoint, above or below, the desired operating value.
A function to overcome this droop was developed and was called Integral, or Reset, and was made a part of the Proportional control. This integrated the error signal as a function of the time during which the offset continued. The amount of Integral effect was preselected by manual adjustment.
Because Proportional control and Proportional plus Integral control could not react quickly to a process with significant dead time (delays in a process change in response to a FCE change), another control mode was developed and added to the analog controller. This function was named Derivative and measures the speed of process variable deviation from setpoint. The controller calculates an addition or subtraction to the control variable based on this deviation speed. The magnitude of derivative action in relation to the speed of deviation is preselected by manual adjustment.
These three modes of control may be adjusted (tuned) to work well on a continuous process, but tend to overshoot above and below setpoint during an initial start-up of a process and will oscillate for many cycles. These oscillations may be extreme enough that the process material is ruined or an unsafe situation occurs.
Multiple attempts have been made to control to a predetermined value (setpoint) without the measured parameter (process variable) exceeding the setpoint using the PID. The original method, and still the most common, to move the process variable to the setpoint is to configure the PID tuning parameters to slow response to process variable disturbance. See FIG. 3. A number of variations to the PID controller have been developed to solve the problem of rapidly moving the process variable, for example, setpoint suppression/reset, ramp/soak, and gap control. Setpoint suppression/reset involves setting an intermediate PID setpoint at some value less than the actual setpoint until the process variable reaches that intermediate setpoint. At that point, the controller setpoint is adjusted to the actual setpoint allowing the process variable to reach that setpoint. A ramp/soak controller moves the PID controller setpoint in small increments (ramps) over time until the controller setpoint reaches the desired setpoint. The controller then holds the process variable at the desired setpoint (soak). See FIG. 4. A gap controller utilizes a PID controller with a downstream “switch” that freezes the final control element when the process variable is within a predetermined band around the setpoint. See FIG. 5.
One of the more recent developments involves using fuzzy logic to anticipate overshoot resulting from the PID calculations. For example, see the patent to Lynch, F. U.S. Pat. No. 5,909,370 (1999) (referred to herein as Lynch). In this method, a fuzzy logic algorithm is used to suppress the setpoint. This is analogous to the setpoint suppression/reset described above. The fuzzy logic algorithm varies the magnitude of the setpoint suppression.
Currently, over 90% of all analog industrial controllers are a form of the PID controller. This controller has been shown to provide the minimum Integrated Average Error (IAE) in continuous control applications where process variable overshoot is acceptable; please see McMillan, G. (1994) Tuning and Control Loop Performance, Instrument Society of America, North Carolina (incorporated herein by reference and referred to herein as McMillan).
The standard PID is also the primary controller used for applications where overshoot is not allowed. However, PID controllers with no-overshoot tuning parameters result in relatively slow performance. See FIG. 3. The reason for this slow performance is that the no-overshoot tuned PID controller begins adjusting the final control element sooner than necessary. Thus, unnecessary time is required to move the process variable to the setpoint. This is because the quantity of controlled material delivered through the final control element, when it is not at its full ON position (or OFF position, if applicable to the specific system), is less than if that control element were fully ON (or OFF) longer.
The most significant shortfall of the traditional PID, when used in applications where overshoot is not allowed, is that the PID does not have a feature ensuring the final control element is set OFF (as used herein, the terms OFF and ON represent succession of the control medium whether the process variable approaches the setpoint from above or below) as the process variable reaches the setpoint. The PID output often does not begin reversing direction (reducing its output after an increasing output) until after the process variable passes the controller's setpoint. Thus, the PID controller does not have systems to prevent or minimize overshoot. Often, a maximum setpoint exists where a process operates optimally. In some cases, however, that process cannot exceed that maximum setpoint without damage occurring to the environment or to the equipment or product. For example, a cereal tastes better when the berry is cooked at 99° C. but the berry's sugar is significantly changed if cooked at 100° C. In the more extreme case of an exothermic reaction, a reactor might explode or the relief devices actuate, if that maximum setpoint is exceeded. Without a method to ensure the final control element is set OFF if the process variable moves beyond the setpoint, the PID controller cannot ensure this damage does not occur. Thus batches can fail and equipment or environmental damage can occur when the PID controller is used for these applications. In these applications, control practitioners often set the operating setpoint below this maximum setpoint. The result is the process does not operate at the optimal point, increasing production times or decreasing production yields.
Setpoint suppression/reset, while commonly utilized in applications where overshoot is not allowed, also has slow performance as the controller first reduces the final control element's percent ON to meet the intermediate setpoint. After the intermediate setpoint is reached, the controller increases the final control element's percent ON to reach the actual setpoint. The controller reduces the percent ON when the process variable reaches the actual setpoint. Extra time is required to reach the actual setpoint than if the controller were able to move the process variable directly to the setpoint.
Ramp/soak controllers are effective in applications in which overshoot is not allowed. Typically, the final control element's percentage ON is in the middle of its percentage ON range. Because the controller's equipment is not immediately positioned at its desired value, the final control element is not held at full ON position for the maximum time while the process variable is approaching setpoint.
While gap controllers ensure the final control element's output is set OFF when the process variable is near the setpoint, the controller acts as an on/off controller near the setpoint. Because of this action, the controller's precision is not the quality of the traditional PID or other controllers.
The fuzzy logic controller proposed by Lynch has the same shortcomings as the setpoint suppression/reset described above along with the added complexity of the fuzzy logic controller.
Fuzzy logic currently is not supported by most industrial controllers and requires significant computing resources to implement.
Thus, a need exists for a controller that moves the process variable to the setpoint more rapidly than PID controllers, yet without overshooting the setpoint.
Feed-Forward Control
Feed-forward control was developed to anticipate control system corrections to process disturbances before the actual process receives the disturbance. Feed-forward control attempts to measure upsets (disturbances) to the process before the upset reaches the process. The controller then calculates corrections for those upsets. An example would be a house having a method to measure whether or not the front door is open and to measure the outside temperature. If the front door opens and a significant difference exist between the outside and inside temperatures, the heating/air conditioning system would start although the inside temperature is presently at the desired value.
The most significant shortfall of the feed-forward controller involves the requirement that the process under control be well understood. Often when implementing these controllers, a disturbance (an event that drives the process from the setpoint) that was not anticipated by the engineer configuring the controller attacks the process. The disturbance can make the process unstable resulting in process or equipment failure or an unsafe condition.
Model-Based Control
The latest developments in process control have been focused on advanced control algorithms including: state-space variable controllers, neural network controllers, artificial intelligence controllers, fuzzy logic controllers etc, further referred to as model-based controllers. Model-based control uses a mathematical representation of an ideally operating process to calculate correction to process upsets. The control practitioner develops the model controller based on anticipated or expected disturbances and the desired process response. Model based control uses a mathematical representation of the process to calculate corrections to process upsets. The model is typically developed using complex mathematical systems such as state-space variable matrices.
As the cost of computing systems is falling, using model-based controllers is becoming more practical. For applications where absolute control system accuracy is necessary, model-based controllers offer significant promise and advancement beyond current technologies.
However, these controllers are very complex and require advanced engineering support to deploy, maintain and modify, increasing the cost of the control system. Because of the complexity of this type of controller, significant computing resources are required to implement these controllers. Most contemporary industrial controllers do not have these computing resources available and those that do are quite expensive. Thus, to date, these controllers have not been widely used in industrial applications.
Contemporary model-based controllers also require that the process under control be well understood and therefore they suffer from the same short coming as feed-forward controllers when the control practitioner overlooks a source of disturbance. As stated above, this disturbance can make the process unstable resulting in process or equipment failure or an unsafe condition. Thus, control practitioners hesitate in implementing these controllers on new processes. In most cases, the control engineer will first install traditional feedback controllers, run the system to ensure all disturbances have been identified and then design the model-based controller. Clearly, the cost to install model-based controllers on new processes can be prohibitive.
Ingredient Addition/Filling Operations
The main analog technique employed to add ingredients or fill products is the full/trickle mode where the control element is set to a “minimum” position as the ingredients near the setpoint. The predominant technique employed to add ingredients or fill products is to start adding the product at full rate. When the added product nears the setpoint, the controller switches to a “trickle” mode in which the product flow is reduced to 10% to 25% of the full rate. When the product quantity is within acceptable error tolerances, the product flow is stopped. This trickle rate is often implemented with a second final control element.
The full/trickle mode method for ingredient addition has worked successfully for many years. It is especially successful when the motive force supplying the ingredients is constant. However, this controller's precision is reduced when that motive force varies. This is because the controller's full OFF point is dependent upon a fixed quantity of material being transferred after the final control element is fully OFF. If that force varies, the quantity of material varies. Another shortcoming of the full/trickle mode for ingredient addition is that, at the predetermined intermediate setpoint, the final control element is set to a reduced percent ON. A better method would have that final control element continuously set OFF as the ingredient quantity approaches the setpoint.
Other Prior Art References:
Traditional control theory texts, such as “Grundlagen der Regelungstechnick” Fundamentals of Control Engineering by Dorrscheidt and Latzel, Teubner-Verlag, Stuttgart, 1993 have referred to using polynomials in feedback control strategies.
While control theory texts have suggested that polynomials would make effective feedback controllers, these controllers applied polynomials in the frequency domain, not the time domain. When frequency domain polynomials of the forms:
                              1                                    s              2                        -                          a              2                                      ⁢                                  ⁢        or        ⁢                                  ⁢                  s                                    s              2                        -                          a              2                                                                      are inverse Laplace transformed back to the time domain, the resultant equations are of the form:
      1    a    ⁢  sin  ⁢          ⁢  at  ⁢          ⁢  or  ⁢          ⁢  cos  ⁢          ⁢  at
These equations result in oscillatory response from the controller, an undesirable result for process control where linear outputs are required. (Note: t is defined in these examples as the error calculation result.) If, in a more general form, the polynomial is of higher order:
                    1                              (                          s              -              a                        )                    n                    ⁢                          ⁢      where      ⁢                          ⁢      n        =    1    ,  2  ,      3    ⁢                  ⁢    …  
The inverse Laplace transform is:
      1                  (                  n          -          1                )            !        ⁢      t          n      -      1        ⁢      ⅇ    at  References such as Beyer, W. (1981), CRC Standard Mathematical Tables, CRC Press, Inc., Boca Raton, Fla. describe inverse Laplace transforms.
This resultant controller equation includes an exponential function (eat). The exponential function, by definition, does not allow the control variable to go to zero. Thus, if the process variable moves past the setpoint, the controller's output would still be greater than zero continuing to add energy or ingredients erroneously.
In order for a controller to be successfully employed in contemporary industrial process controllers (simple software based computing type, traditional electrical/electronic, pneumatic, hydraulic, etc.), the controller's equations need to be time domain based. Though frequency domain type controllers have been used in linear control applications (aircraft control for example) for some time, these controllers require significant computing resources or electronics to deploy. The frequency domain controller is not economically feasible to be utilized for process control applications.
Previous attempts have been made that use an asymptotic approach to setpoint, specifically Rae, Richard, U.S. Pat. No. 4,948,950 (incorporated herein by reference and referred to herein as Rae). However, Rae's method uses a linear algebraic equation for development of the “. . . the target slope below the setpoint temperature or is the target rate of change of the temperature of the output heating effect of the heating means . . . .” Because the equation is a linear function, the process variable does not approach setpoint as quickly as if the equation incorporated an nth-order exponential term. Thus, the control equation proposed by Rae wastes resources, for example time and energy, when applied to a system in which movement of the process variable to setpoint as rapidly as possible, without overshoot, is the key control method selection criteria.